   Chapter 5.CT, Problem 13CT ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
59 views

# In △ M N P ,   N Q → bisects ∠ M N P . If PN = 6, MN = 9, and MP = 10, find PQ and QM. P Q =   _ _ _ _ _ _ _ _ _ _ _ _ Q M =   _ _ _ _ _ _ _ _ _ _ _ To determine

To find:

The value of PQ and QM.

Explanation

Given, MNP,

NQ bisects MNP.

PN = 6, MN = 9, and MP = 10,

By Angle-Bisector theorem:

If a ray bisects one angle of a triangle, then it divides the opposite side into segments whose length are proportional to the lengths of the two sides that form the bisected angle.

i.e. PQPN=QMMN

Let us take, PQ=x

MP=PQ+QM

QM=MP-PQ

QM=10-x

PN = 6, MN = 9, and MP = 10,

Substituting these values in the equation,

PQPN

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